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IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)

Author

Listed:
  • W W Cooper

    (University of Texas at Austin)

  • K S Park

    (University of Ulsan)

  • G Yu

    (University of Texas at Austin)

Abstract

IDEA (Imprecise Data Envelopment Analysis) extends DEA so it can simultaneously treat exact and imprecise data where the latter are known only to obey ordinal relations or to lie within prescribed bounds. AR-IDEA extends this further to include AR (Assurance Region) and the like approaches to constraints on the variables. In order to provide one unified approach, a further extension also includes cone-ratio envelopment approaches to simultaneous transformations of the data and constraints on the variables. The present paper removes a limitation of IDEA and AR-IDEA which requires access to actually attained maximum values in the data. This is accomplished by introducing a dummy variable that supplies needed normalizations on maximal values and this is done in a way that continues to provide linear programming equivalents to the original problems. This dummy variable can be regarded as a new DMU (Decision Making Unit), referred to as a CMD (Column Maximum DMU).

Suggested Citation

  • W W Cooper & K S Park & G Yu, 2001. "IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(2), pages 176-181, February.
    • Handle: RePEc:pal:jorsoc:v:52:y:2001:i:2:d:10.1057_palgrave.jors.2601070
    DOI: 10.1057/palgrave.jors.2601070
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    Citations

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    Cited by:

    1. Zhu, Joe, 2003. "Imprecise data envelopment analysis (IDEA): A review and improvement with an application," European Journal of Operational Research, Elsevier, vol. 144(3), pages 513-529, February.
    2. Avkiran, Necmi K. & Parker, Barnett R., 2010. "Pushing the DEA research envelope," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 1-7, March.
    3. Cui, Qiang & Lin, Jing-ling & Jin, Zi-yin, 2020. "Evaluating airline efficiency under “Carbon Neutral Growth from 2020” strategy through a Network Interval Slack-Based Measure," Energy, Elsevier, vol. 193(C).
    4. Avninder Gill, 2011. "Measurement and Comparison of Productivity Performance Under Fuzzy Imprecise Data," International Journal of Business Research and Management (IJBRM), Computer Science Journals (CSC Journals), vol. 2(1), pages 19-32, April.
    5. K S Park, 2007. "Efficiency bounds and efficiency classifications in DEA with imprecise data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 533-540, April.
    6. William W. Cooper & Kyung Sam Park & Gang Yu, 2001. "An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 49(6), pages 807-820, December.
    7. Shaher Z. Zahran & Jobair Bin Alam & Abdulrahem H. Al-Zahrani & Yiannis Smirlis & Stratos Papadimitriou & Vangelis Tsioumas, 2020. "Analysis of port efficiency using imprecise and incomplete data," Operational Research, Springer, vol. 20(1), pages 219-246, March.
    8. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    9. Castillo, Leopoldo Laborda & Guasch, Jose Luis, 2012. "Overdraft facility policy and firm performance : an empirical analysis in eastern European Union industrial firms," Policy Research Working Paper Series 6101, The World Bank.
    10. K S Park, 2004. "Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1363-1366, December.
    11. R Farzipoor Saen, 2009. "Supplier selection by the pair of nondiscretionary factors-imprecise data envelopment analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1575-1582, November.
    12. José O. Maldifassi & Agustín De la Cuesta W., 2016. "A two-stage process for explaining the relative efficiency of small and medium-size firms in Chile," International Journal of Entrepreneurship and Innovation Management, Inderscience Enterprises Ltd, vol. 20(1/2), pages 99-116.
    13. Park, K. Sam, 2010. "Duality, efficiency computations and interpretations in imprecise DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 289-296, January.
    14. Daniel Sotelsek & Leopoldo Laborda, 2010. "Technical Efficiency and Value Chain of Eastern European Union Companies: An Empirical Application using Semi-Parametric Frontier Methods," Working Papers 04/10, Instituto Universitario de Análisis Económico y Social.
    15. Reza Farzipoor Saen, 2009. "A decision model for ranking suppliers in the presence of cardinal and ordinal data, weight restrictions, and nondiscretionary factors," Annals of Operations Research, Springer, vol. 172(1), pages 177-192, November.
    16. O. Olesen, 2006. "Comparing and Combining Two Approaches for Chance Constrained DEA," Journal of Productivity Analysis, Springer, vol. 26(2), pages 103-119, October.

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